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Testing multipartite productness is easier than testing bipartite productness
- Publication Year :
- 2024
-
Abstract
- We prove a lower bound on the number of copies needed to test the property of a multipartite quantum state being product across some bipartition (i.e. not genuinely multipartite entangled), given the promise that the input state either has this property or is $\epsilon$-far in trace distance from any state with this property. We show that $\Omega(n / \log n)$ copies are required (for fixed $\epsilon \leq \frac{1}{2}$), complementing a previous result that $O(n / \epsilon^2)$ copies are sufficient. Our proof technique proceeds by considering uniformly random ensembles over such states, and showing that the trace distance between these ensembles becomes arbitrarily small for sufficiently large $n$ unless the number of copies is at least $\Omega (n / \log n)$. We discuss implications for testing graph states and computing the generalised geometric measure of entanglement.<br />Comment: 19 pages, 2 figures
- Subjects :
- Quantum Physics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2406.16827
- Document Type :
- Working Paper